If the normal to the parabola y^2=4x at P(1,2 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The given equation of the parabola is $y^2=4x$. For a point $P(x_1, y_1)$ on the parabola $y^2=4ax$,the normal at $P$ is given by $y-y_1 = -\frac{

Vedclass · Accepted Answer

$(9,-6)$

Vedclass · Answer

(B) The given equation of the parabola is $y^2=4x$. For a point $P(x_1, y_1)$ on the parabola $y^2=4ax$,the normal at $P$ is given by $y-y_1 = -\frac{y_1}{2a}(x-x_1)$. Here,$a=1$ and $P=(1,2)$,so the slope of the normal is $m = -\frac{2}{2(1)} = -1$. The equation of the normal at $P(1,2)$ is $y-2 = -1(x-1)$,which simplifies to $x+y=3$,or $x=3-y$. Substituting $x=3-y$ into the parabola equation $y^2=4x$: $y^2 = 4(3-y)$ $y^2 = 12-4y$ $y^2+4y-12=0$ $(y-2)(y+6)=0$ This gives $y=2$ (which corresponds to point $P$) and $y=-6$. For $y=-6$,$x = 3-(-6) = 9$. Therefore,the coordinates of point $Q$ are $(9,-6)$.

If the normal to the parabola $y^2=4x$ at $P(1,2)$ meets the parabola again at $Q$,then the coordinates of $Q$ are

Similar Questions

$A$ hydride of nitrogen which is acidic is

$A$ thin prism $P_1$ with angle $4^o$ and made from a glass of refractive index $1.54$ is combined with another thin prism $P_2$ made from glass of refractive index $1.72$ to produce dispersion without deviation. The angle of the prism $P_2$ is.....$^o$

An object is attached to the bottom of a light vertical spring and set vibrating. The maximum speed of the object is $15 ~cm/s$ and the period is $628 ~ms$. The amplitude of the motion in $cm$ is:

Which of the following is an example of a neutral oxide?

In which of the following reactions,the concentration of product is higher than the concentration of reactant at equilibrium? $(K = \text{equilibrium constant})$

Vedclass Test Series

Exam Paper Generator

Online Exam Module